Clamping devices of the aforementioned type are known in many different variations. One such variation is disclosed in DE 10 2005 005 340 A1. It has a top part with an adjusting mechanism for a clamping arm that can be pivoted into a clamping position and an opening position on the top part. A housing carries the top part and features an interior to accomodate a linearly movable adjusting rod. The adjusting rod is connected to the adjusting mechanism on one end and to a drive arranged in the housing on the other end. The clamping device according to U.S. Pat. No. 5,118,088 A is also based on a similar design. Here, the housing and the top part are manufactured of a profiled section including bores of different diameters. The bores realize a cylinder chamber for a piston drive of the adjusting rod, a guide for the piston rod of smaller diameter and a guide region of slightly larger diameter for the end of the adjusting rod. In another embodiment of the clamping device, illustrated in FIG. 18 of U.S. Pat. No. 5,118,088 A, the housing is one piece including a cylindrical bore except for a remaining bottom structure. The adjusting mechanism is contained in the top part. The clamping arm, connected to the adjusting mechanism, is also arranged on the top part. The top part features an extension that fits into the cylindrical bore of the housing. It has a length that approximately corresponds to half the length of the housing. The extension serves to seal the cylinder chamber and to guide the adjusting rod. In both above-described embodiments, the starting material for the housing consists of an extruded profile that corresponds to the external shape of the housing of the clamping device. It requires complicated internal processing, such as an extruded profile of solid material.